1. Field of the Invention
The present invention relates to electronics, and, in particular, to techniques for tuning and/or measuring operations of an amplifier, such as an operational transconductance amplifier or a variable gain amplifier.
2. Description of the Related Art
FIG. 1 illustrates a block diagram of a conventional circuit 100 for tuning an operational transconductance amplifier (OTA) 102. In addition to OTA cell 102, tuning circuit 100 includes reference OTA cell 101 and comparator 103. The output nodes of OTA cells 101 and 102 are connected together and to the positive input node of comparator 103, which shared node is at voltage Vo,gm.
Vtune is a tuning voltage that is used to adjust the transconductance (gm2) of OTA cell 102. Input voltages V1 and V2 are applied across the input nodes of OTA cells 101 and 102, respectively, where voltages V1 and V2 have identical magnitude, but opposite polarities as indicated in FIG. 1. With voltages V1 and V2 applied with the polarities indicated in FIG. 1, reference OTA cell 101 sources current iout, and OTA cell 102 sinks current iin. If iout equals iin, then the shared node voltage Vo,gm is zero, since voltage Vo,gm corresponds to the current flowing into the positive input node of comparator 103 times the impedance of that input node. If iout≠iin, then the excess current is either sourced or sunk by the positive input node of comparator 103, which causes Vo,gm to be either greater than or less than zero. Because the negative input node of comparator 103 is connected to ground, the output voltage Vout of comparator 103 toggles between a logical 0 and a logical 1 when the value of the difference in current, iout−iin, changes polarity, thus causing the shared node voltage Vo,gm to change its polarity.
A balanced condition occurs when iout=iin and Vo,gm=0. Stated differently, the balanced condition occurs when gm1V1=gm2V2 (i.e., gm2=gm1(V1/V2)). As such, OTA cell 102 may be successfully tuned by adjusting voltage Vtune to determine when such a balanced condition between currents iin, and iout exists by monitoring the output of comparator 103.
FIG. 2 illustrates a more-detailed block diagram of the tuning circuit of FIG. 1. As indicated in FIG. 2, real-world (i.e., actual, physical) implementations of OTA cells 101-102 and comparator 103 include non-idealized electrical properties such as finite output impedances and offsets voltages. In particular, in addition to reference transconductance gm1, reference OTA cell 101 has an offset voltage measured at its input nodes (represented by Vos1 in FIG. 2) and a finite output impedance (represented by go1 in FIG. 2). Similarly, in addition to transconductance gm2 to be tuned, OTA cell 102 has an offset voltage (represented by Vos2 in FIG. 2) and a finite output impedance (represented by go2 in FIG. 2). Comparator 103 also has an offset voltage (represented by Vosc in FIG. 2). By taking all of these non-ideal circuit properties into account, a more-accurate model for the operation of tuning circuit 100 may be developed and transconductance gm2 may be tuned more accurately.
By using node analysis on node Vo,gm, the balanced condition is defined by Equation (1):gm1·(V1+Vos1)=(−Vosc)·(go1+go2)+gm2·(V2+Vos2)  (1)Equation (1) may be rewritten in terms of gm2 as Equation (2):
                              g                      m            ⁢                                                  ⁢            2                          =                                            g                              m                ⁢                                                                  ⁢                1                                      ·                          (                                                                    V                    1                                    +                                      V                                          os                      ⁢                                                                                          ⁢                      1                                                                                                            V                    2                                    +                                      V                                          os                      ⁢                                                                                          ⁢                      2                                                                                  )                                +                                    (                                                V                  osc                                                                      V                    2                                    +                                      V                                          os                      ⁢                                                                                          ⁢                      2                                                                                  )                        ·                          (                                                g                                      o                    ⁢                                                                                  ⁢                    1                                                  +                                  g                                      o                    ⁢                                                                                  ⁢                    2                                                              )                                                          (        2        )            
From Equation (2), transconductance gm2 may be different from transconductance gm1 even with the magnitude of voltage V1 equal to the magnitude of voltage V2. The finite output impedances (go1 and go2) and offset voltages (Vos1 and Vos2) of OTA cells 101 and 102, and the offset voltage (Vosc) of comparator 203 limit the ability to accurately match transconductance gm1 and transconductance gm2. The relative error between transconductance gm2 and reference transconductance gm1 depends on these values as well as on voltages V1 and V2.
Finite output impedance go1 may be made fairly small, since reference OTA cell 101 does not need to process data while in use and, as a result, may be operated slowly. But finite output impedance go2 may correspond to a relatively large fraction of gm2. This condition is especially likely with advanced technologies and high-speed applications. Even without offset voltages Vos1 and Vos2, an error of a few percent may be observed because of the finite output impedances of OTA cells 101-102 and the offset voltage Vosc of comparator 203. This amount of error might not be acceptable for some applications.